Finite Group Databasebeta

← #28402907

Subgroups — #28402907

Order 14464.

398 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299306C211yesmaximal, characteristic, complemented
2#20299266C211yesmaximal, characteristic
3#20298943C211yesmaximal, characteristic, complemented
4#20298913C211yesmaximal, characteristic, complemented
5#20298909C211yesmaximal, characteristic, complemented
6#20298892C211yesmaximal, characteristic, complemented
7#20298847C211yesmaximal, characteristic, complemented
8#20298796C211yesmaximal, characteristic, complemented
9#20298758C211yesmaximal, characteristic, complemented
10#20298757C211yesmaximal, characteristic, complemented
11#20298690C211yesmaximal, characteristic, complemented
12#20298674C211yesmaximal, characteristic, complemented
13#20298600C211yesmaximal, characteristic, complemented
14#20298596C211yesmaximal, characteristic, complemented
15#468×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×#14268646C2211yescharacteristic
18C2×#14268637C2211yescharacteristic
19C2×#14268634C2211yescharacteristic
20C2×#14268630C2211yescharacteristic
21#16813621C2211yescharacteristic
22#16813618—21no—
23#16813618C2211yescharacteristic
24#16813612—21no—
25#16813602—21no—
26#16813599—21no—
27#16813598C2211yescharacteristic
28#16813597C2211yescharacteristic
29#16813595—21no—
30#16813594—21no—
31Q8×Dic113C2211yescharacteristic
32#16813587C2211yescharacteristic
33C4×C22⋊D113C2211yescharacteristic
34#16813582—21no—
35#16813582—21no—
36C2×C4⋊Dic113C2211yescharacteristic
37C4⋊C4×D113C2211yescharacteristic
38#16813555C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813551C2211yescharacteristic
41#16813547C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813545C2211yescharacteristic
44#16813544C2211yescharacteristic
45#16813544C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813542C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×SD16×C113C2211yescharacteristic
53C2×M16×C113C2211yescharacteristic
54C22⋊Q8×C113C2211yescharacteristic
55#121×C113C2211yescharacteristic
56#107×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59#14268647—22no—
60#14268647—41no—
61#14268646—22no—
62#14268646—41no—
63C2×Dic226—21no—
64C2×Dic226C2311yescharacteristic
65C2×D452—21no—
66C2×D452C2311yescharacteristic
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C2×C22⋊D113D411yescharacteristic
72C22×Dic113—21no—
73C22×Dic113—21no—
74C2×C4×D113—21no—
75C2×C4×D113—21no—
76C2×C4×D113C2311yescharacteristic
77#14268637—22no—
78#14268634—41no—
79#14268630—41no—
80C2×#11744751C2311yescharacteristic
81C2×#11744751C2311yescharacteristic
82C4⋊Dic113—21no—
83C4⋊Dic113—21no—
84C4⋊Dic113C2311yescharacteristic
85C4⋊Dic113C2311yescharacteristic
86#14268626—21no—
87#14268626—21no—
88#14268626—21no—
89#14268626—21no—
90#14268626D411yescharacteristic
91C22⋊Dic113D411yescharacteristic
92#14268624—21no—
93#14268624—21no—
94#14268624D411yescharacteristic
95C4×Dic113—21no—
96C4×Dic113—21no—
97C4×Dic113C2311yescharacteristic
98C2×Q8×C113C2311yescharacteristic
99C2×D4×C113—21no—
100C2×D4×C113C2311yescharacteristic
101C22×C4×C113C2311yescharacteristic
102SD16×C113—41no—
103M16×C113—41no—
104C2×C8×C113C2311yescharacteristic
105C2×C8×C113C2311yescharacteristic
106C4⋊C4×C113—21no—
107C4⋊C4×C113C2311yescharacteristic
108C4⋊C4×C113C2311yescharacteristic
109C22⋊C4×C113—21no—
110C22⋊C4×C113—21no—
111C23×C113—21no—
112C23×C113C2×D411yescharacteristic
113C22×D113—21no—
114C22×D113C2×D411yescharacteristic
115Q8×C113—21no—
116Q8×C113—21no—
117D4×C113—21no—
118D4×C113—21no—
119D4×C113—81no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2411yescharacteristic
127C22⋊D113—22no—
128C22⋊D113—42no—
129C22⋊D113—42no—
130C22⋊D113—42no—
131C22⋊D113—81no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134C2×Dic113—21no—
135C2×Dic113—42no—
136C2×Dic113—81no—
137C2×Dic113C2×D411yescharacteristic
138C2×Dic113C2×D411yescharacteristic
139C2×Dic113C2×D411yescharacteristic
140D452—21no—
141D452—21no—
142D452—81no—
143C4×D113—21no—
144C4×D113—21no—
145C4×D113—42no—
146C4×D113—81no—
147Dic226—21no—
148Dic226—81no—
149Dic226#4112yes—
150C8×C113—21no—
151C8×C113—21no—
152#11744751—21no—
153#11744751—21no—
154C22×C113—21no—
155C22×C113—21no—
156C22×C113—21no—
157C22×C113—41no—
158C22×C113—41no—
159C22×C113—41no—
160C22×C113C22×D411yescharacteristic
161C2×D113—21no—
162C2×D113—21no—
163C2×D113—21no—
164C2×D113—41no—
165C2×D113—41no—
166C2×D113—41no—
167C4×C113—21no—
168C4×C113—41no—
169C4×C113—41no—
170C4×C113—41no—
171C4×C113C2×#4111yescharacteristic
172C4×C113H(5,𝔽2)11yescharacteristic
173Dic113—22no—
174Dic113—21no—
175Dic113—21no—
176Dic113—41no—
177Dic113—41no—
178Dic113#13712yes—
179C2×C113—41no—
180C2×C113—81no—
181C2×C113#54611yescharacteristic
182C2×C113C2×#13711yescharacteristic
183C2×C113#57611yescharacteristic
184D113—41no—
185D113—81no—
186#3333—1131nomaximal, Sylow
187C113#333311yescharacteristic, complemented, Sylow
188#554—1131no—
189#550—1131no—
190#486—1131no—
191#480—1131no—
192#480—1131no—
193#477—1131no—
194#468—1131no—
195#468D11311yescharacteristic, complemented
196#460—1131no—
197#452—1131no—
198#452—1131no—
199C4×Q16—1131no—
200#436—1131no—
201#417—1131no—
202#417—1131no—
203C2×#41—1131no—
204C2×#41—1131no—
205C2×Q16—1131no—
206C2×SD16—1131no—
207C2×SD16C2×D11311yescharacteristic
208C2×M16—1131no—
209C2×M16C2×D11311yescharacteristic
210C4⋊Q8—1131no—
211#127—1131no—
212#127—2261no—
213#125—2261no—
214C22⋊Q8—1131no—
215C22⋊Q8—2261no—
216C22⋊Q8—2261no—
217C22⋊Q8C2×D11311yescharacteristic
218#121—1131no—
219#121—2261no—
220#121—2261no—
221#121C2×D11311yescharacteristic
222C4×Q8—1131no—
223C4×Q8—1131no—
224C4×D4—1131no—
225C4×D4—2261no—
226C4×D4—2261no—
227C2×C4⋊C4—1131no—
228C2×C4⋊C4—1131no—
229#107—1131no—
230#107—1131no—
231#107C2×D11311yescharacteristic
232C4⋊C8—1131no—
233#103—1131no—
234#103—1131no—
235#103—1131no—
236#103C2×D11311yescharacteristic
237#102—1131no—
238#102—1131no—
239#102—1131no—
240#102—1131no—
241#102—1131no—
242#102C2×D11311yescharacteristic
243C22⋊C8—1131no—
244C22⋊C8—1131no—
245C4×C8—1131no—
246#41—4521no—
247#41—4521no—
248#41—2262no—
249#41—2262no—
250C2×Q8—1131no—
251C2×Q8—2261no—
252C2×Q8C22×D11311yescharacteristic
253C2×D4—21no—
254C2×D4—1131no—
255C2×D4—1131no—
256C2×D4—2261no—
257C2×D4—2261no—
258C2×D4—2261no—
259C2×D4—2261no—
260C2×D4—2261no—
261C2×D4C22×D11311yescharacteristic
262C22×C4—1131no—
263C22×C4—2261no—
264C22×C4—2261no—
265C22×C4—2261no—
266C22×C4—2261no—
267C22×C4C22×D11311yescharacteristic
268Q16—2262no—
269SD16—41no—
270SD16—4521no—
271M16—41no—
272M16—4521no—
273C2×C8—1131no—
274C2×C8—1131no—
275C2×C8C22×D11311yescharacteristic
276C2×C8C22×D11311yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—1131no—
279C4⋊C4—1131no—
280C4⋊C4—1131no—
281C4⋊C4—2261no—
282C4⋊C4—2261no—
283C4⋊C4—2261no—
284C4⋊C4—2261no—
285C4⋊C4—2261no—
286C4⋊C4—2261no—
287C4⋊C4C22×D11311yescharacteristic
288C4⋊C4C22×D11311yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—1131no—
292C22⋊C4—1131no—
293C22⋊C4—2261no—
294C22⋊C4—2261no—
295C42—1131no—
296C42—2261no—
297C42—2261no—
298C23—21no—
299C23—1131no—
300C23—2261no—
301C23D4×D11311yescharacteristic
302Q8—21no—
303Q8—21no—
304Q8—1132no—
305Q8—9041no—
306Q8—2261no—
307D4—21no—
308D4—21no—
309D4—81no—
310D4—9041no—
311D4—9041no—
312D4—4522no—
313D4—4522no—
314D4—4522no—
315D4—2262no—
316D4—2261no—
317D4—2261no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—1131no—
324C2×C4—1131no—
325C2×C4—1131no—
326C2×C4—9041no—
327C2×C4—9041no—
328C2×C4—4522no—
329C2×C4—4522no—
330C2×C4—2261no—
331C2×C4—2261no—
332C2×C4—2261no—
333C2×C4—2261no—
334C2×C4—2261no—
335C2×C4D4×D11311yescharacteristic
336C2×C4C23×D11311yescharacteristic
337C8—21no—
338C8—21no—
339C8—2261no—
340C8—2261no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—4521no—
348C22—4521no—
349C22—4521no—
350C22—2261no—
351C22—2261no—
352C22—2261no—
353C22C2×D4×D11311yescharacteristic
354C4—21no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—1132no—
359C4—4521no—
360C4—4521no—
361C4—2261no—
362C4—2261no—
363C4—2262no—
364C4#41×D11311yescharacteristic
365C4#1681366711yescharacteristic
366C2—41no—
367C2—81no—
368C2—9041no—
369C2—4521no—
370C2#2029923711yescharacteristic
371C2#137×D11311yescharacteristic
372C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#468×C113C2
socleC22×C113C22×D4
prime radical#20299266C2
hypercenter#468D113
hypocenterC113#3333
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20299306C2semidirect
3. #20298943C2semidirect
4. #20298913C2semidirect
5. #20298909C2semidirect
6. #20298892C2semidirect
7. #20298847C2semidirect
8. #20298796C2semidirect
9. #20298758C2semidirect
10. #20298757C2semidirect
11. #20298690C2semidirect
12. #20298674C2semidirect
13. #20298600C2semidirect
14. #20298596C2semidirect
15. #468×C113C2semidirect
187. C113#3333semidirect
195. #468D113semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202993062
#202992662
#202989432
#202989132
#202989092
#202988922
#202988472
#202987962
#202987582
#202987572
#202986902
#202986742
#202986002
#202985962
#468×C1132
#3333113